A recent article on global warming reminded me of the difficulty of letting the data speak. William Nordhaus shows the following graph:
And then he writes:
One of the reasons that drawing conclusions on temperature trends is tricky is that the historical temperature series is highly volatile, as can be seen in the figure. The presence of short-term volatility requires looking at long-term trends. A useful analogy is the stock market. Suppose an analyst says that because real stock prices have declined over the last decade (which is true), it follows that there is no upward trend. Here again, an examination of the long-term data would quickly show this to be incorrect. The last decade of temperature and stock market data is not representative of the longer-term trends.
The finding that global temperatures are rising over the last century-plus is one of the most robust findings of climate science and statistics.
I see what he’s saying, but first, I don’t find the stock-market analogy to be useful at all—he’s just restating his claim in a different arena, one in which he does not have the laws of physics on his side. Second, the debate over this particular claim is not about what was happening over the last century, it’s about what’s been happening over the past ten years or so.
The (uncomfortable, perhaps) take-home message from the above graph is that it is consistent with a continuing rise in temperature, and it’s also consistent with a leveling-off since the year 2000.
Let me tell you a story. Nearly 25 years ago, Gary King and I came up with an improved estimate of the incumbency advantage in U.S. congressional elections. Here’s the graph summarizing our results:
OK, so what was happening? Incumbency advantage was around 1 percentage point for the first half of the twentieth century, then it steadily rose, with no end in sight as of 1988. Or maybe it rose up until 1966 and then stayed steady after that. Or maybe it rose until 1984 and then flattened out. It’s the climate change story all over again, but this time with a lot less data and no physics to help us out.
Fortunately for our discussion, I returned to estimate the incumbency advantage a few years later, using a better statistical model and more data, going all the way to the year 2000. Here’s what Zaiying Huang and I found (remember, in any given year the estimates will be different, as we use a bigger model and more data):
Hey—it looks like the effect really did peak in the mid-80s, and indeed the declining trend appears to have continued. (I didn’t redo the full analysis but a quick regression gave an estimate of 6 percentage points in 2010.)
Incumbency advantage doesn’t have anything to do with climate change—but the example illustrates the general difficulty of inferring trends from data alone.
To get back to the climate series: the data shown above are consistent with a continuing rise or a flattening of the curve. At this point you have to go to the theory. I think this is how Steven Levitt and Stephen Dubner ended up with the following three statements:
1. “Over the past several years, the average global temperature during that time has in fact decreased.”
2. “Levitt does not believe there is a cooling trend.”
3. Future trends are “virtually assuring us of about 30 years of global cooling.”
These positions are difficult to reconcile as stated, but they can work if you interpret them more vaguely. The time trend is consistent with an increase, no trend, or even a future decrease. That’s why you need to bring in the albedo, if you will. Everybody knows this—scientists don’t study these climate time series in isolation—but then there can be a tendency to oversimplify as in Nordhaus’s discussion quoted above, which implies that the graph tells the story all by itself. The graph is consistent with the story, which counts for something.
P.S. If you’re interested in the incumbency advantage in itself and not merely as an example of a difficult time series, see here for further discussion.